A152996 9 times pentagonal numbers: 9*n*(3*n-1)/2.

0, 9, 45, 108, 198, 315, 459, 630, 828, 1053, 1305, 1584, 1890, 2223, 2583, 2970, 3384, 3825, 4293, 4788, 5310, 5859, 6435, 7038, 7668, 8325, 9009, 9720, 10458, 11223, 12015, 12834, 13680, 14553, 15453, 16380, 17334, 18315, 19323

Offset

0,2

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = A000326(n)*9 = A062741(n)*3.

G.f.: 9*x*(1+2*x)/(1-x)^3. - Colin Barker, Feb 21 2012

a(0)=0, a(1)=9, a(2)=45, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 14 2016

E.g.f.: 9*x*(2 + 3*x)*exp(x)/2. - G. C. Greubel, Sep 01 2019

Maple

seq(9*n*(3*n-1)/2, n=0..40); # G. C. Greubel, Sep 01 2019

Mathematica

Table[9n(3n-1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 45}, 40] (* Harvey P. Dale, Jan 14 2016 *)

Prog

(Magma) [9*n*(3*n-1)/2: n in [0..50]];
(PARI) a(n)=9*n*(3*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [9*n*(3*n-1)/2 for n in (0..40)] # G. C. Greubel, Sep 01 2019
(GAP) List([0..40], n-> 9*n*(3*n-1)/2); # G. C. Greubel, Sep 01 2019

Crossrefs

Cf. A000326 (pentagonal numbers), A062741 (pentagonal numbers multiplied by 3).

Sequence in context: A139609 A321779 A068314 * A188351 A220443 A289721

Adjacent sequences: A152993 A152994 A152995 * A152997 A152998 A152999

Keyword

easy,nonn

Author

Omar E. Pol, Dec 22 2008

Status

approved